Fast Gradient-Based Algorithms for Constrained Total Variation Image Denoising and Deblurring Problems

This paper studies gradient-based schemes for image denoising and deblurring problems based on the discretized total variation (TV) minimization model with constraints. We derive a fast algorithm for the constrained TV-based image deburring problem. To achieve this task, we combine an acceleration o...

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Veröffentlicht in:IEEE transactions on image processing Jg. 18; H. 11; S. 2419 - 2434
Hauptverfasser: Beck, A., Teboulle, M.
Format: Journal Article
Sprache:Englisch
Veröffentlicht: New York, NY IEEE 01.11.2009
Institute of Electrical and Electronics Engineers
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Schlagworte:
Acceleration
Algorithms
Anisotropic magnetoresistance
Applied sciences
Constraints
Convergence
Convex optimization
Deburring
Detection, estimation, filtering, equalization, prediction
Exact sciences and technology
fast gradient-based methods
image deblurring
Image denoising
Image processing
Image restoration
Information, signal and communications theory
Iterative algorithms
Iterative methods
Mathematical models
Miscellaneous
Noise reduction
Optimization
Signal and communications theory
Signal processing
Signal, noise
Tasks
Telecommunications and information theory
Television
total variation
Performance evaluation
Image processing
Threshold detection
Noise reduction
Iterative method
image deblurring
Image restoration
Blurred image
Convex programming
Projection method
fast gradient-based methods
Television
Convex optimization
Signal processing
Numerical simulation
total variation
Fast algorithm
Reliability
Gradient method
Image denoising
ISSN:1057-7149, 1941-0042, 1941-0042
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Beschreibung
Zusammenfassung:This paper studies gradient-based schemes for image denoising and deblurring problems based on the discretized total variation (TV) minimization model with constraints. We derive a fast algorithm for the constrained TV-based image deburring problem. To achieve this task, we combine an acceleration of the well known dual approach to the denoising problem with a novel monotone version of a fast iterative shrinkage/thresholding algorithm (FISTA) we have recently introduced. The resulting gradient-based algorithm shares a remarkable simplicity together with a proven global rate of convergence which is significantly better than currently known gradient projections-based methods. Our results are applicable to both the anisotropic and isotropic discretized TV functionals. Initial numerical results demonstrate the viability and efficiency of the proposed algorithms on image deblurring problems with box constraints.
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ISSN:1057-7149
1941-0042
1941-0042
DOI:10.1109/TIP.2009.2028250